Sound power level calibration of reference sound source in NMIJ

Ryuzo Horiuchi and Keisuke Yamada

National Metrology Institute of Japan National Institute of Advanced Industrial Science and Technology, Japan

Calibration service

Reference Sound Source Type 4204 (Brüel & Kjær)

Power-supply voltage / frequency 100 V / 50 Hz 100 V / 60 Hz

Frequency range of calibration 100 Hz ~ 10 kHz (1/3 octave band)

Reference Sound Source (RSS)

Calibration method

Absolute method in hemi-free field

Comparison method in diffuse sound field

Calibration of RSS of NMIJ Calibration of RSSs of clients

Calibration system for absolute method Calibration system for comparison method

Absolute method in hemi-free field

Hemi-anechoic environment is realized by laying down wooden boards on a wire meshed floor of the anechoic room

Absolute method in hemi-free field according to ISO 6926 and ISO 3745

Fixed microphone array (20 points) Radius of measurement hemisphere: 2.0 m Size of anechoic room : W 9.5 m × D 8.0 m × H 7.2 m (H 5.6 m from floor) Surface density of floor : 15.0 kg/m2 Calibration system for absolute method

Influence of Floor Vibration caused by RSS Operation

RSS was isolated from the floor by hanging the RSS from the ceiling of the anechoic room

RSS Wooden board floor

Wire mesh floor

Measurement hemisphere

Steel wire

1 cm apart from the floor

Schematic view of the measurement

Influence of Floor Vibration caused by RSS Operation

∆𝐿𝐿𝑊𝑊 = 𝐿𝐿𝑊𝑊_hang −𝐿𝐿𝑊𝑊_on

Difference of sound power level

LW_hang: Sound power level with hanging RSS LW_on : Sound power level with RSS on the floor

Difference of sound power level between with/without hanging. Error bars represent standard deviations.

• Differences are less than 0.1 dB • Influence of floor vibration is not significant

Influence of Sound Power Transmission through Floor

RSS Wooden board floor

Microphone

Wire Meshed floor

θ

Acoustic Center

Transmission wave

Reflection wave

Measurement hemisphere

θmax

Schematic view of sound incident in calibration system =𝑊𝑊0

2� 𝜏𝜏𝜃𝜃 𝑓𝑓,𝑚𝑚 sin𝜃𝜃 𝑑𝑑𝜃𝜃𝜃𝜃max

0

𝑊𝑊trans = � 𝜏𝜏𝜃𝜃 𝑓𝑓,𝑚𝑚 𝑰𝑰 ∙ 𝒏𝒏𝑑𝑑𝑑𝑑𝑆𝑆

• Transmitted sound power

I [W/m2]: Sound intensity on dS n: Normal vector of dS W0 [W]: Total sound power emitted from RSS

𝜏𝜏𝜃𝜃 𝑓𝑓,𝑚𝑚 =1

1 + 𝑓𝑓𝑚𝑚𝑍𝑍 cos𝜃𝜃

2

• Transmission coefficient of sound power for sound incident angle θ [rad]

f [Hz]: Sound frequency m [kg/m2]: Surface density of floor Z [kg/m2s]: Acoustic impedance of air

Influence of Sound Power Transmission through Floor

Theologically estimated decrease of sound power level. Surface density of floor was set to 7.5 kg/m2 ,15.0 kg/m2

∆𝐿𝐿𝑤𝑤(𝑚𝑚) = 𝐿𝐿𝑊𝑊measure(𝑚𝑚) − 𝐿𝐿𝑊𝑊0

• Estimated decrease of sound power level with surface density m

With our calibration system (surface density: 15.0 kg/m2), the estimated decrease of sound power level is within 0.15 dB

LW_meausre [dB]: Measurable sound power level

LW0 [dB]: Sound power level of RSS

Experimental evaluation of sound power transmission

𝐿𝐿𝑊𝑊_measure|7.5

−𝐿𝐿𝑊𝑊_measure |15.0

∆𝐿𝐿𝑤𝑤 7.5 − ∆𝐿𝐿𝑤𝑤 15.0

Experimental difference

Theoretical difference Theoretical and experimental result. Error bars represent standard deviations of experimental difference.

Sound power level measurements with two surface densities (15.0 kg/m2 and 7.5 kg/m2)

Compare

The experimental and the theoretical results showed good agreement

Correction for sound power transmission

𝐿𝐿𝑊𝑊 = 𝐿𝐿𝑝𝑝 + 10 log10𝑑𝑑1𝑑𝑑0

+ 𝐶𝐶1 + 𝐶𝐶2 + 𝐶𝐶3 + 𝐶𝐶4

Additional correction for sound power transmission

Sound power level calculation in ISO 3745

Comparison method in diffuse field

Comparison method in hemi-free field according to ISO 3745

Fixed microphone array (6 points)

Volume of reverberation room : 350 m3 Reverberation time: 10 s (at 1000 Hz)

Comparison method using RSS calibrated by absolute method in hemi-free field as reference

Calibration system for comparison method

Equivalency between absolute method and comparison method

Difference of sound power level measured by absolute method and comparison method is within 0.2 dB

Calibration uncertainty

Frequency Uncertainty (k = 2) 100 Hz 0.8 dB 125 Hz 0.6 dB

160 Hz, 200 Hz 0.5 dB 250 Hz ≤ f ≤ 2.5 kHz 0.4 dB

3.15 kHz ≤ f ≤ 5.0 kHz 0.5 dB 6.3 kHz, 8.0 kHz 0.6 dB

10 kHz 0.9 dB

Expanded uncertainty of RSS calibration with comparison method

Request from RSS users

ISO 3745: Precise method to determine the sound power level in an anechoic or hemi-anechoic room Annex A of ISO 3745: Procedure to qualify the performances of anechoic and hemi-anechoic room by estimating the deviation of the sound pressure level from the inverse-square law.

What kind of sound source is suitable for the room evaluation based on ISO 3745?

Measurement of inverse square law

Sound pressure levels were measured along straight paths from the sound source to the room walls.

Sound Source

Steel wire

Microphone

Schematic view of measurement of inverse square law

ISO 3745 requires almost omnidirectional sound source for the measurement

Commercially available loudspeakers usually do not satisfy the requirement

Calculation of effect of directivity

𝑝𝑝 𝒓𝒓 = 𝑝𝑝d 𝒓𝒓 2 + �𝑝𝑝r𝑖𝑖 𝒓𝒓 25

𝑖𝑖=1

= 𝑤𝑤 𝜑𝜑,𝜃𝜃 ∙𝑝𝑝0𝒓𝒓

2+ � 𝑤𝑤 𝜑𝜑𝑖𝑖 ,𝜃𝜃𝑖𝑖 ∙

𝑝𝑝0 1 − 𝛼𝛼𝒓𝒓 − 𝒓𝒓𝒊𝒊

25

𝑖𝑖=1

Schematic of a hemi-anechoic room including the coordinates of the sound source, the mirror image of the sound source.

How does the directivity of sound sources affect on the measurement of inverse square law?

α: sound energy absorption coefficient of walls

𝒓𝒓: position vector

𝑤𝑤 𝜑𝜑,𝜃𝜃 : weighting function representing the directivity of the sound source

𝑝𝑝0: sound pressure averaged over a hemisphere with a radius of unit length and enclosing the sound source

Directivity of RSS

Directivity index of the RSS (Brüel & Kjær type 4202) for elevation angles from 0°to 90° (a) 100 Hz to 400 Hz, (b) 500 Hz to 2000 Hz, and (c) 2.5 kHz to 10 kHz.

-10

-5

0

580°

70°60°

50°

40°

30°

20°

10°

0°

Dire

ctiv

ity in

dex

[dB]

(a) 90°

-10

-5

0

580°

70°60°

50°

40°

30°

20°

10°

0°Di

rect

ivity

inde

x [dB

]

(b) 90°

-10

-5

-0

580°

70°60°

50°

40°

30°

20°

10°

0°

Dire

ctiv

ity in

dex[

dB]

(c) 90°

1/3 octave band frequency Allowable deviation in directivity ≤ 630 Hz

800 Hz to 5 kHz 6.3 kHz to 10 kHz

> 10 kHz

±2.0 dB ±2.5 dB ±3.0 dB ±5.0 dB

Allowable deviation in directivity of the sound source (hemi-free field)

Deviation from inverse square law

Calculated deviation of the sound pressure level from the inverse-square law for the RSS and for the omnidirectional sound source. The sound energy absorption coefficient of walls: 0.95.

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1Devi

atio

n of

soun

d pr

essu

re le

vel

from

the

inve

rse s

quar

e law

[dB]

Normalized distance from sound source

Omnidirectional sound source (independent of frequency)

RSS at 500 Hz

RSS at 1250 Hz

1/3 octave band frequency Allowable deviation in directivity ≤ 630 Hz

800 Hz to 5 kHz > 6.3 kHz

±2.5 dB ±2.0 dB ±3.0 dB

Allowable deviation from inverse square law (hemi-free field)

Influence of directivity of RSS In

dex

∆(r)

[dB]

(a) (b)

Inde

x ∆(

r) [d

B]

(c)

Inde

x ∆(

r)[d

B]

-0.2

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1

Normalized distance from sound source

100 Hz 125 Hz 160 Hz200 Hz 250 Hz 315 Hz400 Hz

-0.2

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1

Normalized distance from sound source

500 Hz 630 Hz 800 Hz1000 Hz 1250 Hz 1600 Hz2000 Hz

-0.2

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1

Normalized distance from sound source

2500 Hz 3150 Hz 4000 Hz5000 Hz 6300 Hz 8000 Hz10000 Hz

Influence of directivity of RSS (a) 100 Hz to 400 Hz, (b) 500 Hz to 2000 Hz and (c) 2.5 kHz to 10 kHz.

Influence of directivity

1/3 octave band frequency

Allowable deviation in directivity

≤ 630 Hz 800 Hz to 5 kHz

> 6.3 kHz

±2.5 dB ±2.0 dB ±3.0 dB

Allowable deviation from inverse square law (hemi-free field)

Conclusion

The analytical results by the proposed method showed that the commercially available RSS can be used for qualifying hemi-anechoic rooms Further studies will aim to examine individual differences of directional characteristics between RSSs of the same type